Lattice dynamics across the magnetic transition in ${\text{(Mn,Fe)}}_{1.95}\text{(P,Si)}$

The lattice dynamics in ${\mathrm{MnFe}}_{0.95}{\mathrm{Si}}_{0.50}{\mathrm{P}}_{0.50}$ were investigated experimentally using ${}^{57}\mathrm{Fe}$ nuclear inelastic scattering and inelastic x-ray scattering across the first-order magnetic transition which occurs close to room temperature. The lattice dynamics characterization was supported by a macroscopic magnetic characterization, an x-ray diffraction study, and a hyperfine interactions characterization using Mössbauer spectroscopy. The Fe specific and the x-ray generalized density of phonon states were obtained both in the ferromagnetic and in the paramagnetic state. A prominent shift, $2\text{meV}$ at $20\text{meV}$, in the x-ray generalized density of phonon states across the first-order magnetic transition, that involves vibrations with essentially Fe character, is revealed corroborated by a change in the local environment quantified in the isomer shift and the quadrupole splitting. Above $35\text{meV}$ the vibrational modes are practically insensitive to the magnetic transition. The entropy change induced by a $1\text{T}$ magnetic field across the magnetic transition, $\sim 10\mathrm{J}/\mathrm{K}/\mathrm{kg}$, is only a fraction of the Fe vibrational entropy change, $62\left(21\right)\mathrm{J}/\mathrm{K}/\mathrm{kg}$.

Figure 1

(Left axis): Isofield magnetization data of ${\mathrm{MnFe}}_{0.95}{\mathrm{Si}}_{0.50}{\mathrm{P}}_{0.50}$ (black tics) measured at ${\mu }_{0}H=1\text{T}$ between 5 and $380\text{K}$ during cooling and heating. (Right axis): The (negative) first derivative of the corresponding magnetization data. Inset: Isothermal magnetization data measured between 0 and $5\text{T}$ every $2\text{K}$ between $361\text{K}$ (blue tics) and $373\text{K}$ (red tics) during heating are depicted in the Arrot plot. Lines between points are given as a guide to the eye. Error bars are smaller than the marker size.

Figure 2

X-ray diffraction pattern of ${\mathrm{MnFe}}_{0.95}{\mathrm{Si}}_{0.50}{\mathrm{P}}_{0.50}$ (black points) measured experimentally at $295\text{K}$, the refinement (red line), the refinement residuals (blue line), and the reflection positions for the (Mn,${\mathrm{Fe})}_3\mathrm{Si}$ impurity phase (magenta tics).

Figure 3

${}^{57}\mathrm{Fe}$-Mössbauer spectra of ${\mathrm{MnFe}}_{0.95}{\mathrm{Si}}_{0.50}{\mathrm{P}}_{0.50}$ (black tics) measured in the ferromagnetic phase at $295\text{K}$ (lower panel) and in the paramagnetic phase at $480\text{K}$ (upper panel), the corresponding model (black line), and the components used in the model (color lines); see text for details.

Figure 4

(Middle panel): The Fe specific density of phonon states (DPS) measured on ${\mathrm{MnFe}}_{0.95}{\mathrm{Si}}_{0.50}{\mathrm{P}}_{0.50}$ in the ferromagnetic (FM) state at $250\left(20\right)\text{K}$ (blue squares) and in the paramagnetic state (PM) at $490\left(20\right)\text{K}$ (red squares) using nuclear inelastic scattering. Inset: The same data in the Debye setting, DPS/$E^2$, are shown below $10\text{meV}$. The solid lines correspond to the Debye level extracted by fitting the data with a constant between 1 and $5\text{meV}$. (Top panel): The x-ray generalized DPS measured on the same sample and at the same temperature using inelastic x-ray scattering; see text. Characteristic error bars are given. (Lower panel): The difference between the DPS measured in the PM state and the DPS measured in the FM state using both nuclear inelastic scattering (black marker) and inelastic x-ray scattering (green marker).